This invention relates to bandpass filter networks and particularly to networks of this type that include double-resonator monolithic crystal filter sections or elements. Monolithic piezoelectric filters are crystal elements which, with their attached resonators, serve as filters without additional components and are old and well-known in the art as illustrated in U.S. Pat. No. 3,564,463 to Beaver et al issued Feb. 16, 1971. As stated therein, in order to avoid complex filters resulting from duplication of crystal structures and extra components, attempts have been made to combine the characteristics of two crystal resonators acoustically by mounting two sets of electrodes on a single body. Thus, the characteristics of the crystal structure were controlled such that the structure alone, monolithically, was capable of performing many of the functions previously performed by whole networks incorporating such crystal structures. Further, practical polylithic filter devices, that is, filters utilizing a plurality of monolithic crystals, have been disclosed as, for example, in U.S. Pat. No. 3,676,806 issued July 11, 1972.
A new class of filter function of the nonminimum phase type was developed by J. D. Rhodes as disclosed in a paper entitled "A Low Pass Prototype Network for Microwave Linear Phase Filters," IEEE Transactions on Microwave Theory and Techniques, MTT-18, Pages 290-301 (June 1970). This filter function offers optimized amplitude and phase responses with functions of lower order and without the use of additional equalizers. However, the Rhodes filter, while offering excellent theoretical performance, has not been realizable for practical applications due to problems with the impedance inverters and monolithic bridging elements caused by inefficient energy storage or figure of merit, Q, of practical inductors. For example, severe degradation of performance is caused by the Q's associated with actual components.